Graphing Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have one solution?

Back

It means the lines intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the lines coincide, or are the same line.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point where the lines intersect on a graph.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as rise over run.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How do you find the slope of a line given two points?

Back

Use the formula: (y2 - y1) / (x2 - x1).

Front

What is the significance of parallel lines in a system of equations?

Back

Parallel lines have the same slope and will never intersect, indicating no solution.

Front

What is the significance of intersecting lines in a system of equations?

Back

Intersecting lines indicate that there is a unique solution to the system.